| 摘要: |
| 本文研究（α，δ）-弱刚性环上的Ore扩张环R[x；α，δ]的弱对称性、弱zip性、幂零p.p.性和幂零Baer性.利用对多项式的逐项分析的方法，证明了如果R是（α，δ）-弱刚性环和半交换环，则Ore扩张环R[x；α，δ]是弱对称的（弱zip的，幂零p.p.的，幂零Baer的）当且仅当R是弱对称的（弱zip的，幂零p.p.的，幂零Baer的）.这些结果统一和扩展了前面已有的相关结论. |
| 关键词: (α,δ)-弱刚性环 Ore扩张 弱对称环 弱zip环 幂零p.p.环 幂零Baer环 |
| DOI： |
| 分类号:O153.3 |
| 基金项目:Supported by the National Natural Science Foundations of China (41275117) and the NSF of Jiangsu Province of China (BK20141476). |
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| ORE EXTENSIONS OVER (α,δ)-WEAKLY RIGID RINGS |
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WANG Yao1, ZHANG Jiu-lin1, REN Yan-li2
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1.School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;2.School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China
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| Abstract: |
| In this paper, we investigate the weak symmetric, weak zip, nilpotent p.p. and nilpotent Baer property of the Ore extension R[x; α,δ] of a ring R, respectively. By using the itemized analysis method on polynomials, we prove that if R is (α,δ)-weakly rigid and semicommutative, then R[x; α,δ] is weak symmetric (resp., weak zip, nilpotent p.p., nilpotent Baer) if and only if R is weak symmetric (resp., weak zip, nilpotent p.p., nilpotent Baer). These results unify and extend nontrivially the previously known results. |
| Key words: (α,δ)-weakly rigid ring Ore extension weak symmetric ring weak zip ring nilpotent p.p.-ring nilpotent Baer ring |
